Sierra College CIE-01 Jim Weir 530.272.2203 Lesson 04 [email protected] www.rstengineering.com/sierra Capacitors Inductors Antennas Capacitors A capacitor is two conductors separated by an insulator. That's pretty generic, isn't it? For example, you are a salt water sack (conductor) separated from your lab partner by an insulator (air). Does that make you two a capacitor? You bet. How about your automobile (steel) separated from the earth (conductor) by rubber tires? Yup (anybody old enough to remember "grounding straps"?). How about the earth and the moon separated by space? You bet. Going to the other extreme, how about two copper atoms separated by the "nothingness" of a billionth of an inch inside the copper molecule? You got it. One of the first capacitors was the Leyden jar, so named because it was invented by Pieter van Musschenbroek of the University of Leyden, Netherlands in 1745. It consisted of an outer metal shell, a glass jar, and an inner metal plate. Two brass conductors separated by a glass insulator. Because at the time it was thought to "condense" the "vapors of electricity" into a jar, it was originally called a "condenser", a name that was used for this electrical device up until the 1950s when the modern word capacitor became the preferred nomenclature. Page 1 of 16 Benjamin Franklin (late, of Philadelphia) did some experimentation with atmospheric static electricity. Franklin used the static electricity to first attract the small pith ball to the Leyden jar's "bell", and then after it was charged, it was repelled to the "grounding" bell, then reattracted to the jar bell, and so on until the static charge was dissipated. In this manner, Franklin could just listen to find out when his kite was in an area of greater electrical activity. Again, as we said in the first lesson, Franklin was no fool. He did NOT fly his kite in a thunderstorm, but flew it when thunderstorms had passed through and charged the atmosphere. Page 2 of 16 If you remember nothing else about capacitors, remember that they store charge and pass AC but block DC. Let's talk about the various things that affect the value of the capacitor, which is measured in "farads" (after Michael Faraday). The farad is far too large of a value to use, since it is based on the coulomb which (as we saw in Lesson 1) is a LOT of electrons. We will use the microfarad (one millionth of a farad), the nanofarad (one billionth of a farad) and the picofarad (one trillionth of a farad) as common units of capacitance. If we have a large plate area, we have "space" for a lot of electrons, and thus larger plates = more capacitance. If the plates are squeezed closer together, the more electrons are attracted to the opposite plate and thus the more capacitance. Think of it as the dance where the little boy electrons and the little girl electrons get closer and closer together … oh, you get the idea. If an insulator with a greater dielectric constant is inserted between the plates, then it "focuses" the electrons and thus increases the capacitance. Page 3 of 16 Here is a table of some common dielectrics and their constants (all measured relative to a vacuum with constant 1.0000): Material Relative permittivity (dielectric constant) ============================================================ Vacuum -------------------------------- 1.0000 Air -------------------------------------- 1.0006 Gasoline ------------------------------- 1.94 Mylar ----------------------------------- 2.0 PTFE, FEP ("Teflon") ---------------- 2.0 Polypropylene ------------------------ 2.20 to 2.28 ABS resin ----------------------------- 2.4 to 3.2 Polystyrene --------------------------- 2.45 to 4.0 Waxed paper ------------------------- 2.5 Transformer oil ---------------------- 2.5 to 4 Hard Rubber ------------------------- 2.5 to 4.80 Wood (Oak) -------------------------- 3.3 Silicones ------------------------------ 3.4 to 4.3 Bakelite ------------------------------- 3.5 to 6.0 Quartz, fused ------------------------- 3.8 Wood (Maple) ----------------------- 4.4 Glass ---------------------------------- 4.9 to 7.5 Castor oil ----------------------------- 5.0 Wood (Birch) ------------------------ 5.2 Mica ---------------------------------- 5.0 to 8.7 Porcelain ----------------------------- 6.5 Alumina ------------------------------ 8.0 to 10.0 Distilled water ----------------------- 80.0 Barium titanite ("ceramic") -------- 7500 One trick that is widely used is to use aluminum foil for one plate of the capacitor and a liquid conducting electrolyte to form aluminum oxide on the plate. This hyper-thin layer of oxide acts as the dielectric in an ELECTROLYTIC capacitor. Electrolytic capacitors are generally the most capacitance in the smallest size possible. Page 4 of 16 Here is a picture of a few different kinds of capacitors: Electrolytic, ceramic, and plastic (left to right) So how do I calculate the value of a capacitor if I know all these values? Quite simply C0.224* * n 1 * A / d Where C is the value of the capacitor in picofarads, ε is the dielectric constant, n is the number of plates, A is the area of one plate in square inches, and d is the distance between the plates in inches. For example, if I have two sheets of tinfoil a foot square separated by a mylar ("saran wrap") sheet 0.0005" thick, I will have C0.224*2*1*144 / 0.0005 128,824 pf or . about .129 nf What are your odds of doing this right, the first time, using a hand Making Inductors and Capacitors calculator? Did I hear "nearly Jim Weir zero"? Exactly correct. What do we 02-Jan-01 use when we have a nasty equation that may give us fits? Did I hear frequency 120.0E+6 Hertz "spreadsheet"? Correct again. Go to your engineering spreadsheet file Number of plates 2 and find the Excel spreadsheet Area of one plate 144 Square inches makeL&C.xls, input the values for Dielectric constant 2 k the capacitor, and see if the sheet Distance between plates 500.0E-6 inches doesn't come out like this (don't worry about "frequency" or Xc yet): Capacitance 129.0E-9 farads Xc 10.3E-3 ohms Well, now I know how to make capacitors and what their values will be, but so what? What is the use of a capacitor in an electronic circuit? Quite simply, a capacitor attempts to keep the VOLTAGE IN A CIRCUIT CONSTANT. If the supply voltage goes UP, it accepts more electrons to try and keep that voltage down, and if the voltage goes DOWN it supplies electrons to keep the voltage up. Thus, if a voltage is noisy, by means of a capacitor we can strip that noise from the voltage, making a nice quiet circuit. Page 5 of 16 Another use of capacitors in a circuit is to set some sort of TIMING. Circuits that oscillate (generate some sort of signal or frequency waveform) almost all use a capacitor as their timing mechanism in some manner. How does this come about? Because of the famous "RC time constant". Here we see a battery (Vs) connected to a switch and then to a resistor and capacitor in series. The question becomes, what happens at the moment the switch is thrown to connect the battery to the resistor? The answer is that the capacitor will start to charge and will get to 63% of the battery voltage in one "time constant". What is a time constant? It is simply the product of R and C (τ = R*C). It will get to 85% of the battery voltage in two time constants. It will, for all practical purposes, become equal to the battery voltage in five time constants. If you would like to see a practical example of how to use capacitors, go to www.rstengineering.com/kitplanes/ and look at the June, July, and August 2000 issues for details on how to build a fuel gauge using capacitors. How does that work going the other way? That is, if the capacitor is fully charged, and if I replace the battery with a short circuit, what will the voltage across the capacitor look like after the switch is thrown? Pretty much the inverse of the charging equations. Now the capacitor will come to 37% of the battery voltage within one time constant, 15% of the battery voltage in two time constants, and for all intents and purposes be at zero volts within 5 time constants. Now if we replace the "switch" with something that does the "switching" automatically (the classic "555" timer is a case in point) we have a capacitor that sets the frequency of oscillation. Page 6 of 16 Finally, we can use our capacitor to tune a radio to a particular station. If we make the plates of the capacitor so that one stays in position while the other one is rotated in or out of the fixed plates, we can vary the capacitance and (as we will see in a bit) vary the RESONANT frequency of the coil (L1) and capacitor (C1). Note that C1 has an ARROW going through it. This denotes a VARIABLE capacitor. The world's first "transistor radio" was made by Regency and called the TR-1. It cost $50 in 1954 dollars, or about $450 in today's money. Rather than beat this horse to death, you may wish to visit this site for some interesting insights into capacitors: http://micro.magnet.fsu.edu/electromag/electricity/capacitance.html/ Page 7 of 16 While we are at it, since capacitors can store voltages and in some cases store lethal quantities of voltage and current, here are some simple rules to remember when the voltage starts getting quite high (say, above 30 volts or so): The Commonsense Rules (for voltages above 30 volts). a. Work thee with a partner that he may pluck thy mangled body from the innards of the equipment.